The figure shows a block of mass m = 2.0 kg attached to a spring with spring con

Question

The figure shows a block of mass m = 2.0 kg attached to a spring with spring constant k on a frictionless surface. The block is pushed to the left to position x = -0.5 m and, at time t = 0, it is released from rest and starts oscillating with a period of 2.0 s.

The figure shows a block of mass m = 2.0 kg attached to a spring with spring constant k on a frictionless surface. The block is pushed to the left to position x = -0.5 m and, at time t = 0, it is released from rest and starts oscillating with a period of 2.0 s.

Explanation / Answer

t =0 x= -0.5

x(t) = -0.5*cos(w*t)

(w) omega = 2pi/T = 2pi / 2 = pi

xt = -0.5 *cos( pi *t)

maximum speed =A*omega = 0.5* pi =0.5 *pi = pi/2 m/s

spring constant   

w = sqrt( k/m)

pi = sqrt( k/2)

k = 2* pi^2 = 2p^2

total energy = 1/2* k*x^2 = 1/2* 2p^2 * 0.5^2 = p^2 /4 J   

in your option pi => p

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